Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/455

 842.] PERFECTLY CONDUCTING MOLECULES. 423

comes, when exposed to external magnetic force, a current-sheet, the action of which on every point of the interior is such as to make the magnetic force zero.

It may assist us in understanding this case if we observe that the distribution of magnetic force in the neighbourhood of such a body is similar to the distribution of velocity in an incompressible fluid in the neighbourhood of an impervious body of the same form.

It is obvious that if other conducting shells are placed within the first, since they are not exposed to magnetic force, no currents will be excited in them. Hence, in a solid of perfectly conducting material, the effect of magnetic force is to generate a system of currents which are entirely confined to the surface of the body.

841.] If the conducting body is in the form of a sphere of radius r, its magnetic moment is

-ir&amp;gt;JT,

and if a number of such spheres are distributed in a medium, so that in unit of volume the volume of the conducting matter is , then, by putting ^=1, and ^ = in equation (1 7), Art. 314, we find the coefficient of magnetic permeability,

2 ~ U/, (9)

��whence we obtain for Poisson s magnetic coefficient


 * =-**, (10)

and for Neumann s coefficient of magnetization by induction

��_

Since the mathematical conception of perfectly conducting bodies leads to results exceedingly different from any phenomena which we can observe in ordinary conductors, let us pursue the subject somewhat further.

842.] Returning to the case of the conducting channel in the form of a closed curve of area A, as in Art. 836, we have, for the moment of the electromagnetic force tending to increase the angle 0,

sme, (12)

smflcosfl. (13)

j

This force is positive or negative according as is less or greater than a right angle. Hence the effect of magnetic force on a per fectly conducting channel tends to turn it with its axis at right

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